Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270103004785/ta1399sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270103004785/ta1399Isup2.hkl | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270103004785/ta1399IIsup3.hkl |
Small single crystals of (I) and (II) were grown by the vapor-diffusion technique (Henisch, 1996) at controlled temperature (293 K) and pH (9). Two saturated solutions containing molar ratios of 2:1:1 of Li2SO4, Cs2SO4 and Rb2SO4 and 1:0.1 of Li2SO4 and Cs2SO4 were prepared in distilled and de-ionized water, thus producing small crystals of (I) and (II), respectively.
Colorless prismatic single crystals of both compounds were selected with the aid of a polarizing microscope. The occupancies of the cations were refined initially and then fixed for the final refinement. Occupancies for (I) were found to be Cs2 0.15 (2), Li2 0.32 (3), Li3 0.20 (2) and Li4 0.40 (3). Occupancies for (II) were found to be Cs 0.90 (1), Rb 0.22 (1), Li1 0.94 (2) and Li2 0.94 (2).
Data collection: Collect (Enraf–Nonius, 1997-2000) for (I); Collect (Nonius BV, 1997-2000) for (II). Cell refinement: HKL SCALEPACK (Otwinowski & Minor, 1997) for (I); HKL SCALEPACK (Otwinowski & Minor 1997) for (II). Data reduction: HKL DENZO and SCALEPACK (Otwinowski & Minor, 1997) for (I); HKL DENZO and SCALEPACK (Otwinowski & Minor 1997) for (II). For both compounds, program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: WinGX publication routines (Farrugia, 1999).
Cs1.15Li2.85(SO4)2 | F(000) = 337 |
Mr = 364.77 | Dx = 2.872 Mg m−3 |
Orthorhombic, Pmc21 | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: P 2c -2 | Cell parameters from 17795 reflections |
a = 5.0620 (2) Å | θ = 1.0–27.5° |
b = 5.2230 (3) Å | µ = 5.55 mm−1 |
c = 16.0060 (9) Å | T = 293 K |
V = 423.18 (4) Å3 | Prism, colorless |
Z = 2 | 0.29 × 0.19 × 0.08 mm |
KappaCCD diffractometer | 1065 independent reflections |
Radiation source: fine-focus sealed tube | 1053 reflections with I > 2σ(I) |
Horizonally mounted graphite crystal monochromator | Rint = 0.032 |
Detector resolution: 9 pixels mm-1 | θmax = 27.5°, θmin = 2.5° |
ϕ scans and ω scans with κ offsets | h = −6→6 |
Absorption correction: multi-scan multi-scan from symmetry-related measurements SORTAV (Blessing, 1995) | k = −6→6 |
Tmin = 0.290, Tmax = 0.661 | l = −20→20 |
1740 measured reflections |
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0969P)2 + 0.7843P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.044 | (Δ/σ)max = 0.006 |
wR(F2) = 0.133 | Δρmax = 0.96 e Å−3 |
S = 1.07 | Δρmin = −0.87 e Å−3 |
1064 reflections | Extinction correction: SHELXL, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
109 parameters | Extinction coefficient: 0.166 (17) |
1 restraint | Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881 |
Primary atom site location: structure-invariant direct methods | Absolute structure parameter: 0.50 (6) |
Cs1.15Li2.85(SO4)2 | V = 423.18 (4) Å3 |
Mr = 364.77 | Z = 2 |
Orthorhombic, Pmc21 | Mo Kα radiation |
a = 5.0620 (2) Å | µ = 5.55 mm−1 |
b = 5.2230 (3) Å | T = 293 K |
c = 16.0060 (9) Å | 0.29 × 0.19 × 0.08 mm |
KappaCCD diffractometer | 1065 independent reflections |
Absorption correction: multi-scan multi-scan from symmetry-related measurements SORTAV (Blessing, 1995) | 1053 reflections with I > 2σ(I) |
Tmin = 0.290, Tmax = 0.661 | Rint = 0.032 |
1740 measured reflections |
R[F2 > 2σ(F2)] = 0.044 | 1 restraint |
wR(F2) = 0.133 | Δρmax = 0.96 e Å−3 |
S = 1.07 | Δρmin = −0.87 e Å−3 |
1064 reflections | Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881 |
109 parameters | Absolute structure parameter: 0.50 (6) |
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger. |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Cs1 | 0.0000 | 0.73578 (12) | 0.73304 (8) | 0.0435 (4) | |
Cs2 | −0.5000 | 0.7927 (15) | 0.8695 (9) | 0.076 (2) | 0.15 |
S1 | 0.0000 | 0.3338 (5) | 0.9399 (3) | 0.0342 (6) | |
S2 | 0.5000 | 0.2659 (4) | 0.6459 (2) | 0.0323 (7) | |
O11 | 0.0000 | 0.6152 (18) | 0.9503 (6) | 0.052 (2) | |
O12 | −0.105 (4) | 0.2508 (16) | 0.8594 (11) | 0.044 (3) | 0.50 |
O13 | −0.292 (3) | 0.2743 (19) | 0.9397 (11) | 0.045 (3) | 0.50 |
O14 | −0.122 (2) | 0.806 (2) | 0.5115 (9) | 0.041 (3) | 0.50 |
O21 | 0.5000 | 0.5347 (16) | 0.6273 (6) | 0.063 (3) | |
O22 | −0.412 (3) | 1.222 (2) | 0.7254 (14) | 0.046 (3) | 0.50 |
O23 | −0.3666 (18) | 1.1020 (19) | 0.5844 (9) | 0.048 (2) | 0.50 |
O24 | −0.206 (4) | 1.2204 (19) | 0.6371 (13) | 0.045 (3) | 0.50 |
Li1 | 0.0000 | 0.146 (3) | 0.5411 (12) | 0.036 (3) | |
Li2 | −0.5000 | 1.168 (6) | 0.8464 (14) | 0.025 (4) | 0.65 |
Li3 | −0.5000 | 0.889 (9) | 0.631 (2) | 0.025 (4) | 0.40 |
Li4 | −0.5000 | 0.786 (4) | 0.924 (2) | 0.036 (3) | 0.80 |
U11 | U22 | U33 | U12 | U13 | U23 | |
Cs1 | 0.0462 (5) | 0.0380 (5) | 0.0463 (5) | 0.000 | 0.000 | 0.0003 (4) |
Cs2 | 0.078 (6) | 0.058 (4) | 0.092 (8) | 0.000 | 0.000 | 0.001 (4) |
S1 | 0.0343 (11) | 0.0330 (13) | 0.0355 (11) | 0.000 | 0.000 | 0.0007 (10) |
S2 | 0.0358 (15) | 0.0280 (13) | 0.0332 (15) | 0.000 | 0.000 | −0.0006 (9) |
O11 | 0.065 (5) | 0.051 (5) | 0.041 (4) | 0.000 | 0.000 | 0.001 (4) |
O12 | 0.049 (8) | 0.049 (8) | 0.035 (6) | −0.019 (4) | −0.022 (6) | 0.006 (4) |
O13 | 0.030 (6) | 0.047 (6) | 0.057 (8) | −0.004 (4) | 0.007 (6) | 0.001 (5) |
O14 | 0.028 (5) | 0.028 (4) | 0.068 (7) | −0.002 (4) | −0.013 (5) | −0.012 (5) |
O21 | 0.112 (8) | 0.034 (4) | 0.043 (4) | 0.000 | 0.000 | 0.016 (4) |
O22 | 0.055 (6) | 0.063 (6) | 0.022 (7) | −0.006 (4) | −0.001 (6) | 0.001 (5) |
O23 | 0.045 (5) | 0.045 (5) | 0.053 (5) | 0.006 (4) | 0.027 (6) | −0.004 (6) |
O24 | 0.032 (7) | 0.035 (5) | 0.067 (9) | 0.006 (5) | −0.012 (6) | −0.008 (5) |
Li1 | 0.041 (7) | 0.021 (6) | 0.046 (8) | 0.000 | 0.000 | 0.004 (5) |
Li2 | 0.031 (9) | 0.025 (12) | 0.018 (9) | 0.000 | 0.000 | −0.009 (7) |
Li3 | 0.031 (9) | 0.025 (12) | 0.018 (9) | 0.000 | 0.000 | −0.009 (7) |
Li4 | 0.041 (7) | 0.021 (6) | 0.046 (8) | 0.000 | 0.000 | 0.004 (5) |
Cs1—O24 | 3.138 (14) | S1—O11 | 1.479 (10) |
Cs1—Li3 | 3.12 (2) | S1—O13 | 1.509 (15) |
Cs1—O21 | 3.221 (6) | S2—O21 | 1.435 (8) |
Cs1—O22 | 3.285 (15) | O12—O13 | 1.60 (2) |
Cs1—O12 | 3.285 (13) | O22—O24 | 1.76 (3) |
Cs2—Li4 | 0.87 (3) | O22—Li2 | 2.01 (3) |
Cs2—Li2 | 1.99 (3) | O22—Li3 | 2.35 (4) |
Cs2—O11 | 2.990 (8) | O23—O24 | 1.33 (2) |
Cs2—O13 | 3.116 (15) | O23—Li3 | 1.50 (4) |
Cs2—O22 | 3.25 (2) | O24—Li3 | 2.29 (4) |
S1—O12 | 1.461 (15) | Li2—Li4 | 2.35 (4) |
O24—Cs1—O21 | 105.5 (4) | O13—O12—Cs2 | 63.9 (7) |
Li3—Cs1—O21 | 116.4 (6) | Cs1—O12—Cs2 | 59.5 (3) |
O21—Cs1—O22 | 136.9 (4) | S1—O13—Cs2 | 98.8 (5) |
O24—Cs1—O12 | 150.4 (6) | O12—O13—Cs2 | 88.6 (8) |
Li3—Cs1—O12 | 112.9 (8) | S2—O21—Cs1 | 102.1 (3) |
O21—Cs1—O12 | 101.5 (4) | O24—O22—Li2 | 155.3 (13) |
O22—Cs1—O12 | 121.0 (5) | Li2—O22—Li3 | 118.5 (15) |
Li4—Cs2—Li2 | 102.9 (19) | O24—O22—Cs2 | 130.7 (8) |
Li4—Cs2—O11 | 63.6 (6) | Li3—O22—Cs2 | 85.5 (11) |
Li2—Cs2—O11 | 112.6 (4) | O24—O22—Cs1 | 69.6 (6) |
Li4—Cs2—O13 | 66.8 (16) | Li2—O22—Cs1 | 89.9 (9) |
Li2—Cs2—O13 | 157.1 (6) | O24—O23—Li3 | 108.1 (18) |
Li4—Cs2—O22 | 137.4 (17) | O23—O24—O22 | 98.5 (15) |
O11—Cs2—O22 | 113.9 (4) | O22—O24—Li3 | 69.6 (11) |
O13—Cs2—O22 | 144.0 (5) | O23—O24—Cs1 | 98.0 (7) |
O12—S1—O11 | 113.2 (5) | O22—O24—Cs1 | 78.8 (8) |
O11—S1—O13 | 101.8 (4) | Li3—O24—Cs1 | 68.1 (9) |
O12—S1—Cs2 | 70.8 (6) | Cs2—Li2—O22 | 108.4 (12) |
O13—S1—Cs1 | 96.2 (6) | O22—Li2—Li4 | 128.9 (15) |
S1—O11—Cs2 | 105.0 (3) | Li4—Li2—Cs1 | 75.6 (8) |
S1—O11—Cs1 | 93.8 (4) | O23—Li3—O22 | 71.5 (17) |
S1—O12—O13 | 58.9 (9) | O23—Li3—Cs1 | 94.8 (6) |
S1—O12—Cs1 | 104.8 (5) | O24—Li3—Cs1 | 69.0 (5) |
O13—O12—Cs1 | 122.1 (7) | O22—Li3—Cs1 | 72.3 (8) |
S1—O12—Cs2 | 85.8 (7) | Li2—Li4—Cs1 | 69.5 (9) |
Cs0.90Li2.88Rb0.22(SO4)2 | F(000) = 325 |
Mr = 350.53 | Dx = 2.772 Mg m−3 |
Monoclinic, Pc | Mo Kα radiation, λ = 0.71073 Å |
Hall symbol: P -2yc | Cell parameters from 8702 reflections |
a = 5.0530 (2) Å | θ = 1.0–27.5° |
b = 5.1990 (4) Å | µ = 5.75 mm−1 |
c = 15.9840 (8) Å | T = 293 K |
β = 90.297 (3)° | Prism, colorless |
V = 419.90 (4) Å3 | 0.09 × 0.08 × 0.06 mm |
Z = 2 |
KappaCCD diffractometer | 1833 independent reflections |
Radiation source: fine-focus sealed tube | 1810 reflections with I > 2σ(I) |
Horizonally mounted graphite crystal monochromator | Rint = 0.046 |
Detector resolution: 9 pixels mm-1 | θmax = 27.5°, θmin = 2.6° |
ϕ scans and ω scans winth κ offsets | h = −6→6 |
Absorption correction: multi-scan multi-scan from symmetry-related measurements SORTAV (Blessing, 1995) | k = −6→6 |
Tmin = 0.632, Tmax = 0.750 | l = −20→20 |
12898 measured reflections |
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | w = 1/[σ2(Fo2) + (0.0519P)2 + 0.1683P] where P = (Fo2 + 2Fc2)/3 |
R[F2 > 2σ(F2)] = 0.025 | (Δ/σ)max < 0.001 |
wR(F2) = 0.083 | Δρmax = 1.07 e Å−3 |
S = 1.22 | Δρmin = −0.53 e Å−3 |
1833 reflections | Extinction correction: SHELXL, Fc*=kFc[1+0.001xFc2λ3/sin(2θ)]-1/4 |
131 parameters | Extinction coefficient: 0.038 (3) |
2 restraints | Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881 |
Primary atom site location: structure-invariant direct methods | Absolute structure parameter: −0.05 (2) |
Cs0.90Li2.88Rb0.22(SO4)2 | V = 419.90 (4) Å3 |
Mr = 350.53 | Z = 2 |
Monoclinic, Pc | Mo Kα radiation |
a = 5.0530 (2) Å | µ = 5.75 mm−1 |
b = 5.1990 (4) Å | T = 293 K |
c = 15.9840 (8) Å | 0.09 × 0.08 × 0.06 mm |
β = 90.297 (3)° |
KappaCCD diffractometer | 1833 independent reflections |
Absorption correction: multi-scan multi-scan from symmetry-related measurements SORTAV (Blessing, 1995) | 1810 reflections with I > 2σ(I) |
Tmin = 0.632, Tmax = 0.750 | Rint = 0.046 |
12898 measured reflections |
R[F2 > 2σ(F2)] = 0.025 | 2 restraints |
wR(F2) = 0.083 | Δρmax = 1.07 e Å−3 |
S = 1.22 | Δρmin = −0.53 e Å−3 |
1833 reflections | Absolute structure: Flack H D (1983), Acta Cryst. A39, 876-881 |
131 parameters | Absolute structure parameter: −0.05 (2) |
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes. |
Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger. |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Cs | −0.92955 (8) | 0.73641 (5) | 0.43372 (4) | 0.02641 (15) | 0.90 |
Rb | −0.4254 (9) | 0.7880 (7) | 0.5725 (3) | 0.0592 (10) | 0.22 |
S1 | −0.9224 (3) | 0.6654 (2) | 0.14039 (9) | 0.0165 (2) | |
S2 | −0.4230 (2) | 0.26658 (18) | 0.34727 (8) | 0.0150 (3) | |
O11 | −0.9573 (7) | 0.3843 (6) | 0.1509 (2) | 0.0270 (7) | |
O12 | −0.6352 (8) | 0.7213 (6) | 0.1402 (3) | 0.0227 (8) | |
O13 | −1.0442 (10) | 0.7448 (5) | 0.0621 (3) | 0.0230 (9) | |
O14 | −1.0432 (8) | 0.8017 (7) | 0.2113 (2) | 0.0225 (7) | |
O21 | −0.5625 (6) | 0.1038 (6) | 0.2851 (2) | 0.0261 (6) | |
O22 | −0.4782 (7) | 0.5377 (6) | 0.3292 (2) | 0.0300 (7) | |
O23 | −0.1375 (9) | 0.2181 (7) | 0.3416 (3) | 0.0265 (8) | |
O24 | −0.5178 (9) | 0.2059 (8) | 0.4312 (3) | 0.0280 (8) | |
Li1 | −0.4158 (16) | 0.1581 (18) | 0.5448 (5) | 0.0200 (11) | 0.92 |
Li2 | −0.9212 (14) | 1.1540 (15) | 0.2464 (4) | 0.0200 (11) | 0.96 |
Li3 | −1.418 (2) | 0.7820 (16) | 0.2419 (6) | 0.0213 (19) |
U11 | U22 | U33 | U12 | U13 | U23 | |
Cs | 0.0261 (2) | 0.0252 (2) | 0.0280 (2) | −0.00027 (16) | 0.00142 (12) | 0.00056 (15) |
Rb | 0.056 (2) | 0.0536 (19) | 0.068 (3) | −0.0005 (15) | 0.000 (2) | 0.0065 (17) |
S1 | 0.0157 (4) | 0.0152 (5) | 0.0185 (4) | 0.0001 (4) | 0.0000 (3) | −0.0008 (4) |
S2 | 0.0156 (6) | 0.0154 (5) | 0.0138 (5) | 0.0006 (3) | 0.0003 (4) | −0.0004 (3) |
O11 | 0.0370 (18) | 0.0171 (16) | 0.0267 (15) | −0.0031 (14) | −0.0023 (12) | −0.0016 (12) |
O12 | 0.0145 (18) | 0.0337 (18) | 0.0199 (17) | −0.0007 (12) | −0.0008 (14) | −0.0008 (12) |
O13 | 0.022 (2) | 0.027 (2) | 0.0196 (19) | 0.0024 (10) | −0.0027 (16) | 0.0044 (9) |
O14 | 0.0178 (16) | 0.0241 (15) | 0.0257 (17) | −0.0016 (14) | 0.0032 (13) | −0.0076 (14) |
O21 | 0.0240 (15) | 0.0243 (16) | 0.0300 (14) | 0.0054 (13) | −0.0058 (11) | −0.0094 (13) |
O22 | 0.0372 (18) | 0.0184 (15) | 0.0346 (16) | 0.0047 (13) | 0.0067 (13) | 0.0027 (13) |
O23 | 0.0168 (17) | 0.0368 (19) | 0.0259 (18) | 0.0028 (13) | −0.0039 (14) | −0.0055 (14) |
O24 | 0.0247 (19) | 0.0419 (19) | 0.0174 (18) | −0.0035 (15) | 0.0027 (15) | 0.0049 (14) |
Li1 | 0.018 (3) | 0.016 (3) | 0.026 (3) | 0.000 (2) | 0.000 (2) | 0.001 (2) |
Li2 | 0.018 (3) | 0.016 (3) | 0.026 (3) | 0.000 (2) | 0.000 (2) | 0.001 (2) |
Li3 | 0.029 (5) | 0.025 (4) | 0.010 (4) | −0.004 (3) | 0.001 (3) | −0.001 (3) |
Cs—Rbi | 3.365 (5) | O21—Rbv | 3.517 (6) |
Cs—Rb | 3.380 (5) | O21—Csviii | 3.575 (4) |
Rb—Li1ii | 1.975 (10) | O22—Csiii | 3.391 (4) |
Rb—Csiii | 3.365 (5) | O23—Csix | 3.086 (4) |
S1—O13 | 1.452 (5) | O23—Csiii | 3.243 (4) |
S1—O14 | 1.472 (4) | O24—Li1 | 1.900 (9) |
S1—O12 | 1.480 (4) | O24—Rbviii | 3.166 (6) |
S1—O11 | 1.482 (3) | O24—Csviii | 3.208 (4) |
S2—O24 | 1.462 (4) | Li1—Rbviii | 1.975 (10) |
S2—O22 | 1.466 (3) | Li2—O23x | 1.908 (9) |
S2—O23 | 1.468 (5) | Li2—O21ii | 1.930 (8) |
S2—O21 | 1.481 (3) | Li2—O11ii | 1.948 (8) |
O11—Rbiv | 2.818 (6) | Li2—S2ii | 3.039 (7) |
O11—Rbv | 3.104 (6) | Li2—Rbvi | 3.764 (9) |
O11—Csv | 3.532 (3) | Li2—Rbvii | 3.774 (9) |
O12—Rbvi | 2.969 (5) | Li2—Csii | 4.258 (8) |
O12—Rbv | 3.053 (5) | Li3—O22i | 1.912 (9) |
O13—Rbvii | 3.105 (5) | Li3—O21x | 1.953 (10) |
O13—Csv | 3.289 (4) | Li3—O12i | 1.982 (11) |
O13—Rbiv | 3.379 (5) | Li3—S2x | 3.031 (9) |
O13—Csvi | 3.440 (3) | Li3—Rbvii | 3.512 (11) |
O14—Li3 | 1.962 (12) | Li3—Rbiv | 4.015 (10) |
O14—Li2 | 2.012 (9) | Li3—Csi | 4.027 (10) |
O14—Rbvii | 3.627 (6) | ||
O22—Cs—O23x | 105.67 (11) | Li3iii—O12—Rbv | 103.7 (3) |
O22—Cs—O24ii | 76.20 (10) | Li1v—O12—Rbv | 78.8 (3) |
O23x—Cs—O24ii | 66.16 (11) | Rbvi—O12—Rbv | 119.4 (2) |
O22—Cs—O23i | 73.02 (11) | S1—O13—Li1iv | 126.6 (4) |
O23x—Cs—O23i | 110.44 (14) | S1—O13—Rbvii | 115.9 (2) |
O24ii—Cs—O23i | 146.66 (12) | S1—O13—Csv | 104.27 (16) |
O22—Cs—O13xi | 102.79 (10) | Li1iv—O13—Csv | 106.2 (3) |
O23x—Cs—O13xi | 148.66 (13) | Rbvii—O13—Csv | 137.72 (18) |
O24ii—Cs—O13xi | 134.66 (11) | S1—O13—Rbiv | 87.94 (17) |
O23i—Cs—O13xi | 66.00 (10) | Li1iv—O13—Rbiv | 70.9 (3) |
O22—Cs—Rbi | 163.73 (9) | Rbvii—O13—Rbiv | 106.55 (19) |
O23x—Cs—Rbi | 89.82 (12) | Csv—O13—Rbiv | 60.62 (10) |
O24ii—Cs—Rbi | 115.63 (10) | S1—O13—Csvi | 131.7 (2) |
O23i—Cs—Rbi | 97.17 (12) | Li1iv—O13—Csvi | 83.0 (3) |
O13xi—Cs—Rbi | 61.01 (10) | Rbvii—O13—Csvi | 61.64 (10) |
O22—Cs—Rb | 79.71 (11) | Csv—O13—Csvi | 101.16 (12) |
O23x—Cs—Rb | 120.14 (10) | Rbiv—O13—Csvi | 140.36 (17) |
O24ii—Cs—Rb | 57.38 (10) | S1—O14—Li3 | 124.9 (4) |
O23i—Cs—Rb | 127.24 (10) | S1—O14—Li2 | 121.7 (3) |
O13xi—Cs—Rb | 77.63 (11) | Li3—O14—Li2 | 105.8 (3) |
Rbi—Cs—Rb | 97.03 (14) | S1—O14—Cs | 130.4 (2) |
O22—Cs—O22i | 103.95 (10) | Li3—O14—Cs | 84.2 (3) |
O23x—Cs—O22i | 74.74 (10) | Li2—O14—Cs | 76.4 (2) |
O24ii—Cs—O22i | 138.98 (10) | S1—O14—Rbvii | 91.93 (19) |
O23i—Cs—O22i | 42.35 (10) | Li3—O14—Rbvii | 70.8 (3) |
O13xi—Cs—O22i | 85.96 (10) | Li2—O14—Rbvii | 78.3 (3) |
Rbi—Cs—O22i | 74.90 (11) | Cs—O14—Rbvii | 137.58 (14) |
Rb—Cs—O22i | 163.58 (9) | S2—O21—Li2viii | 125.5 (3) |
O22—Cs—O13xii | 136.81 (10) | S2—O21—Li3ix | 123.3 (4) |
O23x—Cs—O13xii | 65.81 (10) | Li2viii—O21—Li3ix | 110.8 (4) |
O24ii—Cs—O13xii | 61.44 (11) | S2—O21—Rbv | 117.51 (19) |
O23i—Cs—O13xii | 150.13 (12) | Li2viii—O21—Rbv | 81.9 (2) |
O13xi—Cs—O13xii | 101.16 (12) | Li3ix—O21—Rbv | 73.7 (3) |
Rbi—Cs—O13xii | 54.28 (10) | S2—O21—Csviii | 96.07 (16) |
Rb—Cs—O13xii | 71.04 (11) | Li2viii—O21—Csviii | 78.2 (2) |
O22i—Cs—O13xii | 113.14 (10) | Li3ix—O21—Csviii | 88.4 (3) |
O22—Cs—O24 | 42.55 (9) | Rbv—O21—Csviii | 146.42 (12) |
O23x—Cs—O24 | 147.75 (11) | S2—O22—Li3iii | 138.8 (4) |
O24ii—Cs—O24 | 102.51 (12) | S2—O22—Cs | 111.33 (18) |
O23i—Cs—O24 | 61.65 (10) | Li3iii—O22—Cs | 107.5 (3) |
O13xi—Cs—O24 | 60.53 (10) | S2—O22—Csiii | 92.36 (17) |
Rbi—Cs—O24 | 121.44 (9) | Li3iii—O22—Csiii | 91.4 (3) |
Rb—Cs—O24 | 67.61 (10) | Cs—O22—Csiii | 103.95 (10) |
O22i—Cs—O24 | 104.01 (10) | S2—O23—Li2ix | 130.3 (4) |
O13xii—Cs—O24 | 137.40 (10) | S2—O23—Csix | 116.3 (2) |
O22—Cs—O11xi | 121.18 (9) | Li2ix—O23—Csix | 92.5 (3) |
O23x—Cs—O11xi | 126.72 (10) | S2—O23—Csiii | 98.38 (18) |
O24ii—Cs—O11xi | 100.16 (9) | Li2ix—O23—Csiii | 108.8 (3) |
O23i—Cs—O11xi | 106.50 (10) | Csix—O23—Csiii | 110.44 (14) |
O13xi—Cs—O11xi | 40.84 (8) | S2—O24—Li1 | 144.7 (4) |
Rbi—Cs—O11xi | 48.15 (10) | S2—O24—Rbviii | 139.0 (3) |
Rb—Cs—O11xi | 53.32 (10) | S2—O24—Csviii | 113.0 (2) |
O22i—Cs—O11xi | 113.19 (9) | Li1—O24—Csviii | 93.5 (3) |
O13xii—Cs—O11xi | 62.96 (9) | Rbviii—O24—Csviii | 64.04 (12) |
O24—Cs—O11xi | 84.05 (8) | S2—O24—Cs | 92.21 (19) |
O22—Cs—O21ii | 54.44 (8) | Li1—O24—Cs | 104.7 (3) |
O23x—Cs—O21ii | 54.97 (10) | Rbviii—O24—Cs | 128.77 (16) |
O24ii—Cs—O21ii | 41.10 (9) | Csviii—O24—Cs | 102.51 (12) |
O23i—Cs—O21ii | 108.08 (10) | O24—Li1—O13xiii | 110.8 (4) |
O13xi—Cs—O21ii | 156.17 (9) | O24—Li1—Rbviii | 109.5 (5) |
Rbi—Cs—O21ii | 141.81 (8) | O13xiii—Li1—Rbviii | 104.1 (4) |
Rb—Cs—O21ii | 90.10 (10) | O24—Li1—O12xi | 122.7 (5) |
O22i—Cs—O21ii | 105.12 (8) | O13xiii—Li1—O12xi | 110.3 (4) |
O13xii—Cs—O21ii | 93.84 (9) | Rbviii—Li1—O12xi | 96.9 (4) |
O24—Cs—O21ii | 95.99 (8) | O24—Li1—Li3xiii | 159.2 (4) |
O11xi—Cs—O21ii | 140.51 (8) | O13xiii—Li1—Li3xiii | 81.0 (4) |
Li1ii—Rb—O11xiii | 112.8 (3) | Rbviii—Li1—Li3xiii | 82.7 (3) |
Li1ii—Rb—O12xii | 41.7 (3) | O12xi—Li1—Li3xiii | 37.1 (3) |
O11xiii—Rb—O12xii | 114.30 (19) | O24—Li1—Rb | 89.7 (4) |
Li1ii—Rb—O12xi | 159.0 (3) | O13xiii—Li1—Rb | 75.0 (3) |
O11xiii—Rb—O12xi | 81.86 (15) | Rbviii—Li1—Rb | 159.2 (5) |
O12xii—Rb—O12xi | 119.4 (2) | O12xi—Li1—Rb | 65.0 (3) |
Li1ii—Rb—O11xi | 113.2 (3) | Li3xiii—Li1—Rb | 76.7 (3) |
O11xiii—Rb—O11xi | 117.1 (2) | O24—Li1—Csix | 78.4 (3) |
O12xii—Rb—O11xi | 77.84 (15) | O13xiii—Li1—Csix | 65.7 (2) |
O12xi—Rb—O11xi | 45.84 (12) | Rbviii—Li1—Csix | 63.5 (3) |
Li1ii—Rb—O13xiv | 37.8 (3) | O12xi—Li1—Csix | 156.4 (4) |
O11xiii—Rb—O13xiv | 75.71 (15) | Li3xiii—Li1—Csix | 122.3 (3) |
O12xii—Rb—O13xiv | 64.54 (13) | Rb—Li1—Csix | 130.8 (3) |
O12xi—Rb—O13xiv | 156.1 (2) | O24—Li1—Csviii | 56.8 (3) |
O11xi—Rb—O13xiv | 141.83 (18) | O13xiii—Li1—Csviii | 149.2 (4) |
Li1ii—Rb—O24ii | 34.5 (3) | Rbviii—Li1—Csviii | 61.9 (3) |
O11xiii—Rb—O24ii | 130.99 (19) | O12xi—Li1—Csviii | 99.0 (3) |
O12xii—Rb—O24ii | 67.58 (14) | Li3xiii—Li1—Csviii | 120.8 (3) |
O12xi—Rb—O24ii | 142.9 (2) | Rb—Li1—Csviii | 128.3 (3) |
O11xi—Rb—O24ii | 111.19 (18) | Csix—Li1—Csviii | 83.68 (17) |
O13xiv—Rb—O24ii | 60.94 (14) | O24—Li1—Csiii | 70.4 (3) |
Li1ii—Rb—Li1 | 159.2 (5) | O13xiii—Li1—Csiii | 47.6 (2) |
O11xiii—Rb—Li1 | 74.42 (18) | Rbviii—Li1—Csiii | 142.5 (4) |
O12xii—Rb—Li1 | 154.9 (2) | O12xi—Li1—Csiii | 114.8 (3) |
O12xi—Rb—Li1 | 36.22 (17) | Li3xiii—Li1—Csiii | 110.4 (3) |
O11xi—Rb—Li1 | 77.37 (18) | Rb—Li1—Csiii | 50.77 (16) |
O13xiv—Rb—Li1 | 139.3 (2) | Csix—Li1—Csiii | 80.51 (15) |
O24ii—Rb—Li1 | 125.9 (2) | Csviii—Li1—Csiii | 126.9 (2) |
Li1ii—Rb—Csiii | 84.9 (3) | O24—Li1—Cs | 50.3 (2) |
O11xiii—Rb—Csiii | 69.01 (12) | O13xiii—Li1—Cs | 116.6 (4) |
O12xii—Rb—Csiii | 125.25 (15) | Rbviii—Li1—Cs | 138.6 (4) |
O12xi—Rb—Csiii | 115.17 (15) | O12xi—Li1—Cs | 76.2 (3) |
O11xi—Rb—Csiii | 153.17 (16) | Li3xiii—Li1—Cs | 109.5 (3) |
O13xiv—Rb—Csiii | 64.08 (12) | Rb—Li1—Cs | 50.20 (15) |
O24ii—Rb—Csiii | 72.08 (13) | Csix—Li1—Cs | 127.1 (2) |
Li1—Rb—Csiii | 79.70 (17) | Csviii—Li1—Cs | 78.72 (14) |
Li1ii—Rb—O13xiii | 140.6 (3) | Csiii—Li1—Cs | 71.77 (14) |
O11xiii—Rb—O13xiii | 44.25 (11) | O23x—Li2—O21ii | 108.0 (4) |
O12xii—Rb—O13xiii | 158.0 (2) | O23x—Li2—O11ii | 117.8 (4) |
O12xi—Rb—O13xiii | 60.34 (12) | O21ii—Li2—O11ii | 114.7 (4) |
O11xi—Rb—O13xiii | 106.15 (14) | O23x—Li2—O14 | 101.9 (4) |
O13xiv—Rb—O13xiii | 106.55 (19) | O21ii—Li2—O14 | 104.6 (4) |
O24ii—Rb—O13xiii | 127.6 (2) | O11ii—Li2—O14 | 108.3 (4) |
Li1—Rb—O13xiii | 34.12 (16) | O23x—Li2—S2ii | 91.1 (3) |
Csiii—Rb—O13xiii | 58.37 (11) | O21ii—Li2—S2ii | 23.38 (14) |
Li1ii—Rb—Cs | 87.1 (3) | O11ii—Li2—S2ii | 111.8 (3) |
O11xiii—Rb—Cs | 153.50 (17) | O14—Li2—S2ii | 125.1 (3) |
O12xii—Rb—Cs | 92.19 (14) | O23x—Li2—Li3 | 70.6 (3) |
O12xi—Rb—Cs | 84.36 (14) | O21ii—Li2—Li3 | 131.9 (4) |
O11xi—Rb—Cs | 65.85 (11) | O11ii—Li2—Li3 | 106.6 (3) |
O13xiv—Rb—Cs | 119.52 (16) | O14—Li2—Li3 | 36.5 (2) |
O24ii—Rb—Cs | 58.58 (12) | S2ii—Li2—Li3 | 141.6 (3) |
Li1—Rb—Cs | 81.09 (17) | O23x—Li2—Li3iii | 125.7 (4) |
Csiii—Rb—Cs | 97.03 (14) | O21ii—Li2—Li3iii | 34.8 (2) |
O13xiii—Rb—Cs | 109.30 (15) | O11ii—Li2—Li3iii | 115.2 (3) |
Li1ii—Rb—Li3xiv | 63.4 (3) | O14—Li2—Li3iii | 71.6 (3) |
O11xiii—Rb—Li3xiv | 81.6 (2) | S2ii—Li2—Li3iii | 58.1 (2) |
O12xii—Rb—Li3xiv | 34.33 (18) | Li3—Li2—Li3iii | 105.1 (3) |
O12xi—Rb—Li3xiv | 106.3 (2) | O23x—Li2—Cs | 56.5 (2) |
O11xi—Rb—Li3xiv | 83.0 (2) | O21ii—Li2—Cs | 71.1 (2) |
O13xiv—Rb—Li3xiv | 62.6 (2) | O11ii—Li2—Cs | 173.6 (3) |
O24ii—Rb—Li3xiv | 96.54 (19) | O14—Li2—Cs | 71.7 (2) |
Li1—Rb—Li3xiv | 137.2 (3) | S2ii—Li2—Cs | 72.34 (15) |
Csiii—Rb—Li3xiv | 123.7 (2) | Li3—Li2—Cs | 69.4 (2) |
O13xiii—Rb—Li3xiv | 123.8 (2) | Li3iii—Li2—Cs | 71.1 (2) |
Cs—Rb—Li3xiv | 124.2 (2) | O23x—Li2—Rbvi | 164.1 (4) |
O13—S1—O14 | 110.6 (2) | O21ii—Li2—Rbvi | 67.6 (2) |
O13—S1—O12 | 110.7 (3) | O11ii—Li2—Rbvi | 55.4 (2) |
O14—S1—O12 | 108.5 (2) | O14—Li2—Rbvi | 94.1 (3) |
O13—S1—O11 | 109.15 (19) | S2ii—Li2—Rbvi | 79.85 (18) |
O14—S1—O11 | 109.7 (2) | Li3—Li2—Rbvi | 124.2 (3) |
O12—S1—O11 | 108.13 (19) | Li3iii—Li2—Rbvi | 59.9 (2) |
O13—S1—Rbv | 102.6 (2) | Cs—Li2—Rbvi | 130.9 (2) |
O14—S1—Rbv | 146.8 (2) | O23x—Li2—Rbvii | 100.7 (3) |
O12—S1—Rbv | 56.27 (15) | O21ii—Li2—Rbvii | 151.2 (3) |
O11—S1—Rbv | 58.28 (15) | O11ii—Li2—Rbvii | 46.6 (2) |
O13—S1—Rbiv | 68.50 (17) | O14—Li2—Rbvii | 70.3 (2) |
O14—S1—Rbiv | 104.50 (17) | S2ii—Li2—Rbvii | 158.4 (3) |
O12—S1—Rbiv | 144.30 (17) | Li3—Li2—Rbvii | 60.0 (2) |
O11—S1—Rbiv | 46.34 (15) | Li3iii—Li2—Rbvii | 124.5 (3) |
Rbv—S1—Rbiv | 88.45 (9) | Cs—Li2—Rbvii | 129.3 (2) |
O13—S1—Csv | 54.63 (14) | Rbvi—Li2—Rbvii | 84.19 (19) |
O14—S1—Csv | 154.96 (17) | O23x—Li2—Csii | 46.1 (2) |
O12—S1—Csv | 96.18 (17) | O21ii—Li2—Csii | 83.3 (2) |
O11—S1—Csv | 64.43 (12) | O11ii—Li2—Csii | 96.5 (3) |
Rbv—S1—Csv | 53.21 (9) | O14—Li2—Csii | 147.1 (3) |
Rbiv—S1—Csv | 52.88 (9) | S2ii—Li2—Csii | 60.10 (13) |
O13—S1—Rbvi | 79.98 (19) | Li3—Li2—Csii | 116.0 (3) |
O14—S1—Rbvi | 97.60 (17) | Li3iii—Li2—Csii | 117.2 (3) |
O11—S1—Rbvi | 144.82 (15) | Cs—Li2—Csii | 81.27 (14) |
Rbv—S1—Rbvi | 86.73 (11) | Rbvi—Li2—Csii | 118.13 (19) |
Rbiv—S1—Rbvi | 146.19 (17) | Rbvii—Li2—Csii | 116.88 (19) |
Csv—S1—Rbvi | 98.94 (9) | O22i—Li3—O21x | 104.5 (5) |
O14—S1—Rbvii | 66.27 (18) | O22i—Li3—O14 | 112.0 (5) |
O12—S1—Rbvii | 119.10 (15) | O21x—Li3—O14 | 114.0 (5) |
O11—S1—Rbvii | 131.47 (15) | O22i—Li3—O12i | 113.8 (5) |
Rbv—S1—Rbvii | 146.24 (17) | O21x—Li3—O12i | 102.7 (5) |
Rbiv—S1—Rbvii | 86.36 (11) | O14—Li3—O12i | 109.5 (5) |
Csv—S1—Rbvii | 98.55 (8) | O22i—Li3—S2x | 98.3 (4) |
Rbvi—S1—Rbvii | 79.43 (8) | O21x—Li3—S2x | 24.10 (17) |
O24—S2—O22 | 109.0 (2) | O14—Li3—S2x | 96.1 (4) |
O24—S2—O23 | 110.2 (3) | O12i—Li3—S2x | 125.6 (4) |
O22—S2—O23 | 109.8 (2) | O22i—Li3—Li1iv | 142.4 (4) |
O24—S2—O21 | 109.6 (2) | O21x—Li3—Li1iv | 105.7 (4) |
O22—S2—O21 | 109.1 (2) | O14—Li3—Li1iv | 74.8 (4) |
O23—S2—O21 | 109.0 (2) | O12i—Li3—Li1iv | 37.3 (3) |
O24—S2—Li3ix | 109.5 (3) | S2x—Li3—Li1iv | 118.1 (3) |
O22—S2—Li3ix | 133.8 (2) | O22i—Li3—Li2 | 121.2 (5) |
O23—S2—Li3ix | 79.2 (3) | O21x—Li3—Li2 | 76.5 (3) |
O24—S2—Li2viii | 99.8 (2) | O14—Li3—Li2 | 37.6 (2) |
O22—S2—Li2viii | 85.6 (2) | O12i—Li3—Li2 | 123.4 (4) |
O23—S2—Li2viii | 138.3 (2) | S2x—Li3—Li2 | 59.3 (2) |
Li3ix—S2—Li2viii | 63.5 (3) | Li1iv—Li3—Li2 | 87.4 (3) |
O24—S2—Csiii | 91.29 (19) | O22i—Li3—Li2i | 104.9 (5) |
O22—S2—Csiii | 64.65 (16) | O21x—Li3—Li2i | 34.4 (3) |
O23—S2—Csiii | 58.83 (15) | O14—Li3—Li2i | 138.0 (4) |
O21—S2—Csiii | 158.87 (15) | O12i—Li3—Li2i | 71.2 (4) |
Li3ix—S2—Csiii | 137.7 (2) | S2x—Li3—Li2i | 58.4 (2) |
Li2viii—S2—Csiii | 150.27 (15) | Li1iv—Li3—Li2i | 88.3 (3) |
O24—S2—Cs | 65.20 (18) | Li2—Li3—Li2i | 105.1 (3) |
O22—S2—Cs | 47.64 (14) | O22i—Li3—Rbvii | 169.9 (5) |
O23—S2—Cs | 142.76 (16) | O21x—Li3—Rbvii | 74.0 (3) |
O21—S2—Cs | 106.98 (14) | O14—Li3—Rbvii | 77.3 (3) |
Li3ix—S2—Cs | 138.0 (2) | O12i—Li3—Rbvii | 57.7 (3) |
Li2viii—S2—Cs | 76.06 (14) | S2x—Li3—Rbvii | 84.2 (2) |
Csiii—S2—Cs | 83.98 (2) | Li1iv—Li3—Rbvii | 33.9 (2) |
O24—S2—Csix | 74.82 (18) | Li2—Li3—Rbvii | 68.5 (2) |
O22—S2—Csix | 149.00 (16) | Li2i—Li3—Rbvii | 68.1 (2) |
O21—S2—Csix | 97.65 (13) | O22i—Li3—Cs | 59.5 (3) |
Li3ix—S2—Csix | 67.0 (2) | O21x—Li3—Cs | 90.6 (3) |
Li2viii—S2—Csix | 124.70 (15) | O14—Li3—Cs | 66.1 (3) |
Csiii—S2—Csix | 84.75 (3) | O12i—Li3—Cs | 166.5 (4) |
Cs—S2—Csix | 138.06 (4) | S2x—Li3—Cs | 67.90 (19) |
O24—S2—Csviii | 47.38 (18) | Li1iv—Li3—Cs | 140.9 (4) |
O22—S2—Csviii | 127.42 (16) | Li2—Li3—Cs | 61.6 (2) |
O23—S2—Csviii | 122.15 (16) | Li2i—Li3—Cs | 121.0 (3) |
O21—S2—Csviii | 62.39 (14) | Rbvii—Li3—Cs | 130.0 (3) |
Li3ix—S2—Csviii | 68.11 (19) | O22i—Li3—Rbiv | 90.0 (3) |
Li2viii—S2—Csviii | 61.46 (14) | O21x—Li3—Rbiv | 150.3 (5) |
Csiii—S2—Csviii | 138.15 (4) | O14—Li3—Rbiv | 82.9 (3) |
Cs—S2—Csviii | 83.36 (3) | O12i—Li3—Rbiv | 47.6 (2) |
Csix—S2—Csviii | 78.656 (18) | S2x—Li3—Rbiv | 171.3 (3) |
S1—O11—Li2viii | 133.2 (3) | Li1iv—Li3—Rbiv | 53.2 (2) |
S1—O11—Rbiv | 111.30 (18) | Li2—Li3—Rbiv | 118.0 (3) |
Li2viii—O11—Rbiv | 103.2 (3) | Li2i—Li3—Rbiv | 117.2 (3) |
S1—O11—Rbv | 97.76 (16) | Rbvii—Li3—Rbiv | 87.1 (3) |
Li2viii—O11—Rbv | 93.5 (3) | Cs—Li3—Rbiv | 119.0 (3) |
Rbiv—O11—Rbv | 117.06 (19) | O22i—Li3—Csi | 45.6 (3) |
S1—O11—Csv | 93.34 (13) | O21x—Li3—Csi | 62.6 (3) |
Li2viii—O11—Csv | 131.1 (3) | O14—Li3—Csi | 144.8 (4) |
Rbiv—O11—Csv | 62.84 (13) | O12i—Li3—Csi | 105.1 (4) |
Rbv—O11—Csv | 60.83 (11) | S2x—Li3—Csi | 67.59 (19) |
S1—O12—Li3iii | 124.6 (4) | Li1iv—Li3—Csi | 140.3 (4) |
S1—O12—Li1v | 127.9 (4) | Li2—Li3—Csi | 122.0 (3) |
Li3iii—O12—Li1v | 105.7 (4) | Li2i—Li3—Csi | 60.3 (2) |
S1—O12—Rbvi | 121.4 (2) | Rbvii—Li3—Csi | 128.4 (3) |
Li3iii—O12—Rbvi | 88.0 (3) | Cs—Li3—Csi | 78.80 (18) |
S1—O12—Rbv | 99.95 (18) | Rbiv—Li3—Csi | 117.8 (2) |
Symmetry codes: (i) x−1, y, z; (ii) x, y+1, z; (iii) x+1, y, z; (iv) x−1, −y+1, z−1/2; (v) x, −y+1, z−1/2; (vi) x, −y+2, z−1/2; (vii) x−1, −y+2, z−1/2; (viii) x, y−1, z; (ix) x+1, y−1, z; (x) x−1, y+1, z; (xi) x, −y+1, z+1/2; (xii) x, −y+2, z+1/2; (xiii) x+1, −y+1, z+1/2; (xiv) x+1, −y+2, z+1/2. |
Experimental details
(I) | (II) | |
Crystal data | ||
Chemical formula | Cs1.15Li2.85(SO4)2 | Cs0.90Li2.88Rb0.22(SO4)2 |
Mr | 364.77 | 350.53 |
Crystal system, space group | Orthorhombic, Pmc21 | Monoclinic, Pc |
Temperature (K) | 293 | 293 |
a, b, c (Å) | 5.0620 (2), 5.2230 (3), 16.0060 (9) | 5.0530 (2), 5.1990 (4), 15.9840 (8) |
α, β, γ (°) | 90, 90, 90 | 90, 90.297 (3), 90 |
V (Å3) | 423.18 (4) | 419.90 (4) |
Z | 2 | 2 |
Radiation type | Mo Kα | Mo Kα |
µ (mm−1) | 5.55 | 5.75 |
Crystal size (mm) | 0.29 × 0.19 × 0.08 | 0.09 × 0.08 × 0.06 |
Data collection | ||
Diffractometer | KappaCCD diffractometer | KappaCCD diffractometer |
Absorption correction | Multi-scan multi-scan from symmetry-related measurements SORTAV (Blessing, 1995) | Multi-scan multi-scan from symmetry-related measurements SORTAV (Blessing, 1995) |
Tmin, Tmax | 0.290, 0.661 | 0.632, 0.750 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 1740, 1065, 1053 | 12898, 1833, 1810 |
Rint | 0.032 | 0.046 |
(sin θ/λ)max (Å−1) | 0.650 | 0.649 |
Refinement | ||
R[F2 > 2σ(F2)], wR(F2), S | 0.044, 0.133, 1.07 | 0.025, 0.083, 1.22 |
No. of reflections | 1064 | 1833 |
No. of parameters | 109 | 131 |
No. of restraints | 1 | 2 |
Δρmax, Δρmin (e Å−3) | 0.96, −0.87 | 1.07, −0.53 |
Absolute structure | Flack H D (1983), Acta Cryst. A39, 876-881 | Flack H D (1983), Acta Cryst. A39, 876-881 |
Absolute structure parameter | 0.50 (6) | −0.05 (2) |
Computer programs: Collect (Enraf–Nonius, 1997-2000), Collect (Nonius BV, 1997-2000), HKL SCALEPACK (Otwinowski & Minor, 1997), HKL SCALEPACK (Otwinowski & Minor 1997), HKL DENZO and SCALEPACK (Otwinowski & Minor, 1997), HKL DENZO and SCALEPACK (Otwinowski & Minor 1997), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), ORTEP-3 for Windows (Farrugia, 1997), WinGX publication routines (Farrugia, 1999).
Double sulfate crystals, (LiASO4, with A = Na, K, Rb, Cs and NH4), have been widely studied due to the rich variety of properties and phase transitions exhibited by these families. Among the compounds with this chemical formula, crystals can be found displaying ferroelectricity (Shiroishi et al., 1976), ferroelasticity (Pakulski et al., 1983), superionic conduction (Karlsson & McGreevy, 1995) and incommensurate phases (Mashiyama et al., 1979). In general, double sulfates crystallize in a tridymite-like structure where A cations are piled along the c axis at the vertices of pseudo-hexagonal networks, which are distributed inside layers of SO4 tetrahedra. Li cations are located at vacancies of the network between the layers (Aleksandrov, 1993).
Two polymorphic families are observed in double sulfate compounds due to distortions of the pseudo-hexagonal lattice. The first corresponds to lattices with hexagonal basis vectors or closely related structures, such as, for example, a monoclinic lattice with ah ≈ bh and β ≈ 120°. Another form of polymorphism is characterized by a set of orthogonal axes, which are related to the hexagonal axes by ao = ah, bo = ah and co = ch, or slight distortions of ??it??, such as a monoclinic lattice with one of the internal angles close to 90°. It is known that the different forms of polymorphism are closely related to the dynamics and possible orientations of the tetrahedral SO4 groups in the structure and the ionic radius of the A cation. As an example of these polymorphs, we show in Fig. 1 the crystal structures of Cs2SO4 and KLiSO4, where the distorted and regular hexagonal lattices can be observed. The A cation lattice dependence is particularly evident in mixed crystals [Li(A'A")SO4], in which the crystal structure and the phase transition sequence are strongly dependent on the concentration and radius of the alkaline cations.
Usually, simple and mixed double sulfates grow from aqueous solutions containing stoichiometric mixtures of the simple sulfate salts Li2SO4·H2O, A'2SO2 and, if necessary, A"2SO4. Generally, alkaline sulfate salts give rise to structures with mainly the same characteristics as double sulfates. However, Li2SO4 and Li2SO4·H2O crystallize in a different structure pattern because the small lithium radius is not able to support the pseudo-hexagonal network, and consequently Li cations are approximately aligned to the basal plane of the SO4 tetrahedra.
Recently, on the basis of X-ray powder diffraction and Raman scattering, a new phase in the LiRbSO4-LiCsSO4 system was characterized (Lima et al., 2000). This phase seems to be stable over variations of the growing conditions. Polarized Raman spectra and X-ray powder diffraction suggest that the crystal structure is monoclinic, with point group Cs. Moreover, the lattice parameters are a = 15.983 (6), b = 5.050 (4), c =5.191 (7) Å and β = 90.22°, which cannot be interpreted as a simple distortion of the tridymite network.
Based on these results, several attempts to grow high-quality single crystals with the structure reported by Lima et al. (2000) were carried out, in order to obtain samples suitable for structure determination. We report here single-crystal X-ray diffraction studies of two crystals obtained from different salt mixtures, with formulae Cs1.15Li2.85(SO4)2 (I) and Cs0.90Li2.88Rb0.22(SO4)2 (II), established from the least-squares refinement, which have structures closely related to those reported by Lima et al. (2000). These structures do not exhibit the same features as most other alkali sulfates, where pseudo-hexagonal networks composed of SO4 and one kind of cation are piled along the c axis (typical of the tridymite-like structures) and the other kind of cation is located at vacancies in the network between the layers (Aleksandrov, 1993).
Compound (I) is orthorhombic, and projections of the structure on the ac and bc planes are shown in Figs. 2a and 2 b. The Cs ions occupy two different Wyckoff positions, a and b. Several refinement tests indicated that atoms in position a have full occupancy, while atoms in position b have partial occupancy [0.15 (2)]. Li ions were refined with their site occupancies constrained such that, together with the Cs ions, the total charge is two. The structure was found to be a racemic twin, the fractional component of the inverted structure being 0.53 (6) (Flack, 1983). Besides the Li and Cs occupational disorder observed in the structure, the O atoms located at the basal plane of the SO4 group are also disordered, thus allowing two possible orientations for this group. As shown in Fig. 2c, O11 atoms are located at the apex site of the tetrahedra centered in S1, while the two possible bases are determined by each set of O21, O12 and O14 atoms. The coordination of the S2 atom is also shown in Fig. 2c and is similar to that around S1.
Compound (II) is monoclinic, and projections of the structure on the ac and bc planes are shown in Figs. 3a and 3 b. The Cs and Rb ions occupy two different general positions, both with partial occupancies. Several refinement tests ruled out the possibility that these sites are shared by both ions. Li ions were refined, as in the previous structure, with their site occupation factors constrained such that, together with the Cs and Rb ions, the total charge is two. No disorder of the SO4 groups was observed in this crystal. Furthermore, the structure is consistent with the previous Raman scattering study, which indicated a monoclinic lattice with Cs symmetry (Lima et al., 2000).
Despite the fact that both refinements were carried out independently with different space groups and chemical formulae, the structures are nearly isomorphous. In fact, each structure can be refined with the diffraction data of the other, although, of course, ?the refinement converges? to higher R1 factors. Via a comparison of both crystal structures (Fig. 2 and 3) it is possible to identify the main similarities and differences between them. Notice that the unit cell of (I) has been shifted by (0,0,1/4) in order to help the comparison. In (II) the monoclinic angle β= 90.297 (2)° may be thought of as a distortion from the orthorhombic 90° angle, which results in the removal of the mirror plane. Cation substitution influences the ordering of the SO4 groups in the crystal structure. In the orthorhombic structure, (I), the SO4 groups are found with two equally probable orientations, while in the monoclinic structure, (II), the SO4 groups are well ordered. Although orientational disorder of the SO4 groups is only observed in (I), the main orientation of these groups is the same as that in (II). Li2 and Li1 do not change their positions relative to the SO4 groups, while in (II), Li3 is almost aligned with Li1, thus forming a plane perpendicular to the [001] direction. The main difference between the two structures can be observed in the Li4 and heavy-cation distribution. In (I), the Cs cations are aligned in the [100] direction, alternating full and partially occupied sites, and the Li4 cations are intercalated among one of the SO4 layers, while in (II) the Rb ions are shifted from the line determined by the Cs cations and partially occupy the Li4 site, ??as Li4 is?? not present in this structure.
Finally, we would like to comment on the reported structures in the context of simple and double sulfate polymorphism. It has been pointed out that double sulfates are characterized by a pseudo-hexagonal network determined by the heavy ions, within which layers of SO4 groups perpendicular to the pseudo-hexagonal axis are distributed. A comparison of structures representative of simple and double sulfate polymorphism (Fig. 1) with the projection of (I) (Fig. 2 b) and (II) (Fig. 3 b) on the bc plane reveals an atomic pattern similar to that observed in the pseudo-hexagonal network; this pattern is represented by dashed lines in the figures. On the basis of this lattice, we can associate the ah and ch hexagonal axis with the ao(am) and bo(bm) axis of the orthorhombic (monoclinic) cell, respectively. Note that the ab pseudo-axis value corresponds approximately to that measured in double sulfates, but the ch pseudo-axis is much shorter. This contraction is due to the low occupation of the heavy-ion sites, which are responsible for the pseudo-hexagonal framework. Furthermore, in the structures reported in this work, the SO4 groups are not intercalated between the planes determined by the heavy ions but lie in the same planes (see Figs. 2a and 3a). The ch-axis contraction does not allow Li ions to be placed on the top of the SO4 tetrahedra (see Fig. 1 b), but the Li ions occupy interstitial sites between these groups. According to the previous discussion, the c axis of the monoclinic and orthorhombic lattices reported in this work should be associated with the bo axis of the orthorhombic polymorphism of sulfate crystals, which is expected to be a multiple of (3)1/2ah. Thus, in spite of the small contraction, it is observed that c≈2(3)1/2a. These results complete the correspondence bewteen the crystal structures of (I) and (II) with the usual polymorphism of the simple and double sulfate crystals.